Compressed-sensing ultrafast spectral photography systems and methods

ABSTRACT

Among the various aspects of the present disclosure is the provision of systems and methods of compressed-sensing ultrafast spectral photography.

CROSS-REFERENCES TO RELATED APPLICATIONS

This application claims priority to and benefit of U.S. ProvisionalPatent Application No. 62/904,442, titled “Compressed-Sensing UltrafastSpectral Photography (CUSP)” and filed on Sep. 23, 2029, which is herebyincorporated by reference in its entirety and for all purposes.

FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT

This invention was made with government support under Grant No(s).EB016986 & CA186567 awarded by the National Institutes of Health. Thegovernment has certain rights in the invention.

FIELD

Certain embodiments generally relate to ultrafast imaging and, morespecifically, certain aspects pertain to compressed-sensing ultrafastspectral photography.

BACKGROUND

Observing extremely fast dynamics requires imaging speeds orders ofmagnitude beyond the maximum reachable by electronic sensors. Thepopular stroboscopic method fails to record events in real time since itdepends on repeated measurements. This limitation is resolved bysingle-shot ultrafast imaging techniques. However, none of thesingle-shot ultrafast imaging techniques have imaging speeds greaterthan 10¹³ frames per second (fps), and most single-shot ultrafastimaging techniques have shallow sequence depths (tens of frames).

SUMMARY

Certain aspects pertain to compressed-sensing ultrafast spectralphotography (CUSP) methods and/or systems that can be used, for example,to image ultrafast phenomena.

Certain aspects pertain to a compressed-sensing ultrafast spectralphotography (CUSP) system for obtaining a series of final recordedimages of a subject. In one implementation, the CUSP system includes anillumination section that includes first and second beam splittersconfigured to receive a first laser pulse and configured to convert thefirst laser pulse into a pulse train that comprises a plurality ofsub-pulses evenly separated in time and an optical component configuredto temporally stretch and chirp each of the sub-pulses of the pulsetrain, where the illumination section is configured to illuminate anobject of interest with the temporally stretched and chirped sub-pulsesof the pulse train to produce a first series of images. In oneimplementation, the CUSP system also includes an imaging section thatincludes a spatial encoding module configured to receive the firstseries of images and to produce a second series of spatially encodedimages, each spatially encoded image of the second series comprising atleast a first view including one image of the first series superimposedwith a pseudo-random binary spatial pattern and a streak camera coupledto the spatial encoding module, the streak camera configured to receivethe second series of spatially encoded images, to deflect each spatiallyencoded image by a temporal deflection distance that varies as afunction of time-of-arrival, and to integrate the temporally-deflectedimages into a single raw CUSP image.

Certain aspects pertain to a compressed-sensing ultrafast spectralphotography (CUSP) system for obtaining a series of final recordedimages of a subject. In one implementation, the CUSP system includes aspatial encoding module configured to receive a first series of imagesand to produce a second series of spatially-encoded images, eachspatially encoded image of the second series comprising at least a firstview including one image of the first series superimposed with apseudo-random binary spatial pattern; an optical element configured toreceive the second series of spatially encoded images and to produce athird series of spatially-encoded and spectrally-dispersed images; and astreak camera configured to receive the third series ofspatially-encoded and spectrally-dispersed images, to deflect eachspatially-encoded and spectrally-dispersed image by a temporaldeflection distance that varies as a function of time-of-arrival, and tointegrate the temporally-deflected images into a single raw CUSP image.

Certain aspects pertain to a method of obtaining a series of finalrecorded images of an object using a compressed-sensing ultrafastspectral photography (CUSP) system. In one implementation, the methodincludes collecting a first series of images of the object;superimposing a pseudo-random binary spatial pattern onto each image ofthe first series to produce a second series of spatially-encoded images;dispersing each image of the second series of spatially-encoded imagesby spectrum to produce a third series of spatially-encoded andspectrally-dispersed images; deflecting each spatially-encoded andspectrally-dispersed image of the third series by a temporal deflectiondistance that varies as a function of a time-of-arrival of eachspatially encoded image to produce a fourth series of time-shearedspatially-encoded spectrally-dispersed images; integrating and recordingthe fourth series of time-sheared spatially-encoded spectrally-dispersedimages as a single raw CUSP image; and reconstructing a fifth series offinal images by processing the single raw CUSP image according to animage reconstruction algorithm.

These and other features are described in more detail below withreference to the associated drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic diagram of components of a compressed-sensingultrafast spectral photography (CUSP) system, according to certainimplementations.

FIG. 2 illustrates a CUSP system imaging an ultrafast linear opticalphenomenon, according to an aspect.

FIG. 3 illustrates a CUSP system imaging an ultrafast nonlinear opticalphenomenon, according to an aspect.

FIG. 4 illustrates a CUSP system imaging an ultrafast fluorescencephenomenon, according to an aspect.

FIG. 5 is a diagram of a streak camera that may be used in a CUSPsystem, according to an aspect.

FIG. 6 includes graphs of various properties of a streak camera that maybe used in a CUSP system, according to an aspect.

FIG. 7 illustrates a pulse train generator that that may be used in aCUSP system, according to an aspect.

FIG. 8 illustrates data captured by a CUSP system, according to anaspect.

FIG. 9 illustrates a data acquisition process of a CUSP system,according to an aspect.

FIG. 10 illustrates spatial and temporal chirps generated by a gratingpair in a CUSP system, according to an aspect.

FIG. 11 is a schematic diagram of components of a compressed-sensingultrafast spectral photography (CUSP) system configured for imagingultrashort pulse propagation in a Kerr medium, according to certainimplementations.

FIG. 12 illustrates data captured by a CUSP system, according to anaspect.

FIG. 13 is a schematic diagram of components of a passivecompressed-sensing ultrafast spectral photography (CUSP) system,according to certain implementations.

These and other features are described in more detail below withreference to the associated drawings.

DETAILED DESCRIPTION

Different aspects are described below with reference to the accompanyingdrawings. The features illustrated in the drawings may not be to scale.In the following description, numerous specific details are set forth inorder to provide a thorough understanding of the presented embodiments.The disclosed embodiments may be practiced without one or more of thesespecific details. In other instances, well-known operations have notbeen described in detail to avoid unnecessarily obscuring the disclosedembodiments. While the disclosed embodiments will be described inconjunction with the specific embodiments, it will be understood that itis not intended to limit the disclosed embodiments. Certain aspectspertain to compressed-sensing ultrafast spectral photography (CUSP)methods and/or systems.

I. Introduction

Cameras' imaging speeds fundamentally limit humans' capability indiscerning the physical world. Countless femtosecond dynamics, such asultrashort light propagation, radiative decay of molecules, solitonformation, shock wave propagation, nuclear fusion, photon transport indiffusive media, and morphologic transients in condensed matters, playpivotal roles in modern physics, chemistry, biology, materials science,and engineering. However, real-time imaging—defined as multi-dimensionalobservation at the same time as the event actually occurs without eventrepetition—requires extreme speeds that are orders of magnitude beyondthe current limits of electronic sensors. Existing femtosecond imagingmodalities either require event repetition for stroboscopic recording(termed the “pump-probe” method) or provide single-shot acquisition withno more than 1×10¹³ frames per second (fps) and 300 frames.

One promising approach to ultrafast imaging is compressed ultrafastphotography (CUP), which creatively combines a streak camera withcompressed sensing. Examples of compressed ultrafast photographymethods, which are hereby incorporated by reference in their entireties,are described by Gao, L. et al., “Single-shot compressed ultrafastphotography at one hundred billion frames per second.” Nature 516, 74-77(2014) and Liang, J. et al., “Single-shot real-time femtosecond imagingof temporal focusing.” Light Sci. Appl. 7, 42 (2018). A streak camera isa one-dimensional (1D) ultrafast imaging device that first convertsphotons to photoelectrons, then temporally shears the electrons by afast sweeping voltage, and finally converts electrons back to photonsbefore they are recorded by an internal camera. In CUP, imagingtwo-dimensional (2D) transient events is enabled by a scheme of 2Dspatial encoding and temporal compression. Unfortunately, CUP's framerate is limited by the streak camera's capability in deflectingelectrons, and its sequence depth (300 frames) is tightly constrained bythe number of sensor pixels in the shearing direction.

The compressed ultrafast spectral photography (CUSP) systems and methodsdescribed herein can overcome the limits of CUP and other ultrafastimaging systems. As an example, CUSP systems and methods cansimultaneously achieve 7×10¹³ fps and 1,000 frames (i.e., sequencedepth). CUSP breaks the limitations in framerate of other ultrafastimaging modalities by employing spectral dispersion in the directionorthogonal to temporal shearing, thereby extending to spectro-temporalcompression. Furthermore, CUSP can achieve a greater sequence depth byexploiting pulse splitting. The CUSP systems and methods may achievesuch results by synergizing spectral encoding, pulse splitting, temporalshearing, and compressed sensing. CUSP is also advantageous inscalability and photon throughput, compared with existing ultrafastimaging technologies. In some configurations, CUSP can function as thefastest single-shot 4D spectral imager (i.e., the fastest single-shotimager that collects (x, y, t, λ) information). As an example, in apassive mode, the CUSP systems and methods may be used achievefour-dimensional (4D) spectral imaging at 0.5×10¹² fps, enablingsingle-shot spectrally-resolved fluorescence lifetime imaging microscopy(SR-FLIM).

CUSP's real-time imaging speed of 70 Tfps (70 trillion frames persecond) in active mode is three orders of magnitude greater than thephysical limit of semiconductor sensors. Owing to this new speed, CUSPcan quantify physical phenomena that are inaccessible using the previousrecord-holding systems. Moreover, active CUSP captures data more than10⁵ times faster than the pump-probe approach. When switching CUSP topassive mode for single-shot SR-FLIM, the total exposure time for oneacquisition (<1 ns) is more than 10⁷ times shorter than that oftime-correlated single photon counting (TCSPC). As a generic hybridimaging tool, CUSP's scope of application far exceeds the demonstrationspresented herein. The imaging speed and sequence depth can be highlyscalable via parameter tuning. CUSP can cover its spectral region fromX-ray to NIR, and even matter waves such as electron beams, given theavailability of sources and sensing devices.

Both the pump-probe and TCSPC methods require event repetition.Consequently, these techniques are not only slower than CUSP by ordersof magnitude as aforementioned, but are also inapplicable in imaging thefollowing classes of phenomena: (1) high-energy radiations that cannotbe readily pumped such as annihilation radiation (basis for PET),Cherenkov radiation, and nuclear reaction radiation; (2)self-luminescent phenomena that occur randomly in nature, such assonoluminescence in snapping shrimps; (3) astronomical events that arelight-years away; and (4) chaotic dynamics that cannot be repeated. Yet,CUSP can observe all of these phenomena. For randomly occurringphenomena, the beginning of the signal can be used to trigger CUSP.

II. Compressed Ultrafast Spectral Photography (CUSP)

FIG. 1 is a schematic diagram of components of a compressed ultrafastspectral photography (CUSP) system 100, according to certainimplementations. In some aspects, CUSP includes two components, animaging section 102 and an optional illumination 104 section. CUSP canbe configured for operation in an active imaging mode and passiveimaging mode. The imaging section is utilized in both the active andpassive imaging modes, while the illumination section is utilized forthe active imaging mode only.

A. Imaging Section

CUSP system 100 includes an imaging section 102. In the imaging section102, a dynamic scene 106 (I(x, y, t, λ)) is imaged by an lens system108. Light from the lens system 108 is then received by beam splitter(BS) 110 and split into two portions. Beam splitter 110 may spilt theincoming light between the two portions evenly, or unevenly with morelight intensity directed toward one portion than the other portion, asdesired. It should be understood that CUSP system 100 may includevarious optical elements such as mirrors M and lenses L, that thedepictions of such optical elements in the figures is merely an exampleof one possible configuration, and that number and placement of suchoptical elements can be varied without changing the principles ofoperation of CUSP system 100.

The first portion of light from the beam splitter 110 may be routedthrough an optical system (e.g., one or more mirrors M, lenses L, and/orother optical elements) toward camera 112, which is configured tocapture a time-unsheared spectrum-undispersed image (defined as u-View).Camera 112 may be, as an example, a CMOS camera. In the example imagingconfigurations described herein, camera 112 was implemented using aPoint Grey camera model GS3-U3-28S4M. Other cameras, including non-CMOScameras, may be utilized in place of camera 112, as desired. Dataacquisition unit 150 may acquire the time-unsheared spectrum-undispersedimage (u-View) from camera 112.

The second portion of light from the beam splitter 110 may be routedtoward a digital micromirror device (DMD) 114. In some configurations,DMD 114 is a DLP® LightCrafter 3000® from Texas Instruments. DMD 114may, in some embodiments, include a plurality of micromirrors, each ofwhich can switch between first and second states. When a micromirror isin the first state, light from the beam splitter 110 that reflects offof that micromirror may be reflected onto an optical path towards streakcamera 116. When a micromirror is in the second state, light from thebeam splitter 110 that reflects off of that micromirror may be reflectedonto another optical path. In some configurations, light that reflectsoff a micromirror in the second state is discarded. In some otherconfigurations, a second streak camera may be provided and light thatreflects off a micromirror in the second state may be reflected onto anoptical path towards the second streak camera. Use of a second streakcamera in this manner may improve spatial resolution and/or temporalresolution of the CUSP system 100 in certain situations.

In some embodiments, DMD 114 may be loaded with a pseudo-random pattern(e.g., each micromirror of DMD 114 may be placed into the first orsecond state in a pseudo-random manner). As a result, the light routedtoward DMD 114 may be encoded according the pseudo-random binary patternloaded into the DMD 114. In some configurations, a static pseudo-randombinary pattern with a non-zero filling ratio of 35% is displayed on theDMD 114. In other embodiments, DMD 114 may be loaded with a non-randompattern. If desired, individual micromirrors within DMD 114 may bebinned together (trading resolution for increased signal). In someconfigurations, DMD 114 may be configured with 3×3 binning (e.g., DMD114 is divided into groups of 3×3 micromirrors, where the micromirrorsin each group are set to a common state). The encoded light may then berelayed to a fully-opened (or partially-opened) entrance port of thestreak camera 116.

Before reaching the streak camera 116, the encoded light from DMD 114may pass through a diffraction grating such as diffraction grating 118(also labeled G in insert a of FIG. 1 ). The diffraction grating 118 mayspectrally disperse the encoded light in a horizontal direction (e.g.,such that the encoded light is dispersed along axis x_(s), when reachingthe entrance slit of streak camera 116). In some configurations, thediffraction grating 118 may spectrally disperse the encoded light in adirection that is orthogonal to the direction of shearing that occurs instreak camera 116. In the configuration of FIG. 1 , higher frequenciesof light are dispersed towards the bottom of FIG. 1 (i.e., in thedirection “away” from streak camera 116 in the insert a of FIG. 1 ),while lower frequencies of light are dispersed towards the top of FIG. 1(i.e., in the direction “towards” streak camera 116 in the insert a ofFIG. 1 ). After the light is reflected off of optional mirror M, thehigher frequencies of light enter into the left side of the entranceslit of streak camera 116, while lower frequencies of light enter intothe right side of the entrance slit of streak camera 116 (in theperspective of the insert a of FIG. 1 ).

During imaging, the streak camera 116 may have a partially or fullyopened slit to capture 2D images. The streak camera 116 converts thearriving photons to electrons at the photocathode, appliestime-dependent shearing to these electrons using a sweeping voltage,converts the electrons back to photons using a phosphor screen,amplifies the photos via an image intensifier, and then integrates thetime-sheared image on an image sensor. Streak camera 116 may also bereferred to as a temporal encoding modulator. Within the streak camera116, the electrons may be temporally sheared in a direction orthogonalto the spectral dispersion imparted by diffraction grating 118. As anexample, the electrons may be sheared in a vertical direction (e.g.,along axis y_(s), a direction into and out of the plane of insert a ofFIG. 1 ). Streak camera 116 may receive the entire, or less than theentire, field of view of the spectrally-dispersed and spatially-encodedimage from diffraction grating 118 and DMD 114, deflect thespectrally-dispersed and spatially-encoded image by a temporaldeflection distance proportional to time-of-arrival, and record thedeflected image as a time-sheared spectrally-dispersed spatially-encodedimage (defined as s-View). The image captured by the internal camerawithin streak camera 116 is time-sheared by streak camera 116,spectrally-dispersed by diffraction grating 118, and spatially-encodedby DMD 114. An example of such a time-sheared spectrally-dispersedspatially-encoded image (e.g., an s-View) is shown in insert b of FIG. 1. The image sensor in the streak camera 116 may be a CMOS camera such asthe Orca R2 from Hamamatsu, as an example. Data acquisition unit 150 mayacquire the time-sheared spectrally-dispersed spatially-encoded image(s-View) from streak camera 116 (e.g., the internal camera of streakcamera 116).

B. Illumination Section

When operating in active mode, an illumination section 104 may encodetime into spectrum, as shown in FIG. 1 . In particular, a broadbandfemtosecond pulse (e.g., a 48-fs, 800 nm wavelength pulse) may begenerated by laser 120. The broadband pulse may be converted to a pulsetrain with neighboring sub-pulses separated by time t_(sp), using a pairof high-reflectivity beam splitters 122. Beam splitters 122 may bepassive optical components. Other examples of passive optical componentsinclude mirrors, lenses, beam splitters, diffraction gratings, glass rod124, and the like. An example of an active optical component includesDMD 114.

A schematic of a pair of beam splitters 902 and 904 in proximity, whichmay serve as beam splitters 122 of FIG. 1 , is shown in FIG. 7 . Beamsplitters 902 and 904 may operate in a non-resonance mode. The timedelay between neighboring sub-pulses may be determined by the physicalgap h_(b):

$\begin{matrix}{t_{sp} = {\frac{2\; h_{b}}{c}{n_{0}.}}} & (1)\end{matrix}$

In equation (1), n₀=1 (for air) and c is the speed of light. Ahigh-precision micrometer stage (shown schematically at stage 154 inFIG. 1 ) may be used to control the position of one beam splitterrelative to the other. Stage 154 may have a step size of 300 nm(equivalent to approximately 2 fs in time delay). In some otherconfigurations, stage 154 may have step size of less than 150 nm, lessthan 150 nm, less than 450 nm, less than 600 nm, less than 750 nm, lessthan 900 nm, or greater than 900 nm or may have a step size in the rangeof 150 nm to 300 nm, in the range of 300 nm to 450 nm, in the range of450 nm to 600 nm, in the range of 600 nm to 750 nm, or in the range of750 nm to 900 nm. Note that the sides of the beam splitters 902 and 904coated with beam splitter coating 906 face the cavity (gap between thebeam splitters) so that all the sub-pulses go through the beam splittersubstrates the same number of times, which is also the minimum number oftimes. To protect the laser cavity from unwanted back-reflection, thebeam splitters may be slightly tilted. In the examples presented here,t_(sp)=2 ps and 2h_(b)=600 μm, which is far below the measured coherencelength of 20 μm. Thus, there is effectively no interference betweenneighboring sub-pulses.

The intensity of each sub-pulse was experimentally measured by thestreak camera 116 at 10 THz sweeping speed. Beam splitters of higherreflectivity may generate more usable sub-pulses, but with a penalty ofreduced pulse energy. Charts b and c of FIG. 7 show the results ofgenerating five and seven usable sub-pulses, respectively. Due to theresponse linearity of the streak camera (as shown in graph c of FIG. 6), the normalized pixel value equals the normalized light intensity. Asthe sub-pulse order p increases, its intensity falls exponentially.Therefore, only the first few sub-pulses are used, while the rest may bediscarded due to the lower intensity, which could lead to a lower SNR.

After conversion of the broadband pulse to a pulse train by beamsplitters 122, the pulse train may be temporally stretched and chirpeach sub-pulse. As an example, the pulse train may be passed through ahomogenous glass rod 124. Since the chirp imparted by glass rod 124 islinear, each wavelength in the pulse bandwidth carries a specific timefingerprint. Thereby, this pulse train is sequentially timed by t(p,λ)=pt_(sp)+η(λ−λ₀), where p=0, 1, 2, . . . , (P−1) represents thesub-pulse sequence, η is the overall chirp parameter, and λ₀ is theminimum wavelength in the pulse bandwidth.

This timed pulse train then illuminates a dynamic scene 106(I(x,y,t)=I(x, y, t(p, λ))), which is subsequently imaged by the imagingsection 102.

In the examples presented here, glass rods 124 of various lengths, madeof N-SF11, were employed to linearly chirp and stretch the femtosecondpulse to a picosecond length. N-SF11 has a group velocity dispersion(GVD) of 187.5 fs²/mm at λ_(c)=800 nm, which is translated to a GVDparameter of D_(λ)=−0.555 fs/(nm/mm) by

$\begin{matrix}{D_{\lambda} = {{- \frac{2\;\pi\; c}{\lambda_{c}^{2}}} \cdot {{GVD}.}}} & (2)\end{matrix}$For a bandwidth of 38 nm, a 270-mm-long N-SF11 rod and a 95-mm-long onestretch the 48-fs pulse to 5.7 ps and 2.0 ps, corresponding to negativechirp parameters of η_(rod_1)=−150 fs/nm and η_(rod_2)=−52.7 fs/nm,respectively. The 270-mm rod and the 95-mm rod were deployed for theexperiments shown in FIGS. 2 and 3 , respectively.

For a bandwidth of 38 nm, a 270-mm-long N-SF11 rod and a 95-mm-long onestretch the 48-fs pulse to 5.7 ps and 2.0 ps, corresponding to negativechirp parameters of η_(rod_1)=−150 fs/nm and η_(rod_2)=−52.7 fs/nm,respectively. The 270-mm rod and the 95-mm rod were deployed for theexperiments shown in FIGS. 2 and 3 , respectively.

Measurements of the pulse train, before and after being stretched, wereobtained and are shown in FIG. 8 . Image a of FIG. 8 was acquired bystreak camera 116 without diffraction grating 118, while image b wasacquired with diffraction grating. Images c, d, and e of FIG. 8 wereacquired with diffraction grating 118 and the streak camera 116operating in 10-THz streak mode. Images c, d, and e of FIG. 8 wereacquired with no glass rod 124, with a 95-mm glass rod 124, and with a270-mm glass rod 124, respectively.

As shown in image a of FIG. 8 , grating 118 disperses a square-shapedobject in the horizontal direction. When there is no rod 124, thetime-sheared image acquired in streak mode resembles that acquired infocus mode. However, a large temporal chirp becomes evident when astretching rod is inserted. The measured time delay between the shortest(785 nm) and the longest (823 nm) wavelengths matched well with thetheoretical predictions. The temporal chirp by a homogeneous isotropicrod can be treated as a linear chirp. This linearity is demonstrated bythe centers of the light intensity distributions at differentwavelengths, which match well with the theoretical estimation based on alinear temporal chirp (solid lines overlaid in the in images c, d, and eof FIG. 8 ). In graphs f and g of FIG. 8 , measurements from anauto-correlator and spectrometer also confirm the stretch. Afterconverting the wavelength to time through the linear chirp parameter,the spectrum (short-dashed line) yields an intensity profile wellmatching the Gaussian-pulse approximation (long-dashed line) derivedfrom the auto-correlator signals.

When operating in active mode, the imaging framerate of CUSP system 100is determined by R_(a)=∥μ∥/(|η|d), where μ is the spectral dispersionparameter of the system, and d is the streak camera's pixel size. Thesequence depth is N_(ta)=PB_(i)|μ|/d, where P is the number ofsub-pulses, and B_(i) is the used spectral bandwidth of the illuminatinglight pulse (785 nm to 823 nm).

C. Image Reconstruction

Computing device 152 may be configured with a CUSP reconstructionalgorithm, may receive the time-unsheared spectrum-undispersed image(u-View) from camera 112, may receive the time-shearedspectrally-dispersed spatially-encoded image (s-View) from streak camera116, and may use these images in reconstructing individual image frames.As part of reconstructing the sequence images, computing device 152 mayalso utilize the pattern loaded into DMD 114. In some configurations,computing device 152 may be coupled to DMD 114, configured to loadpatterns into DMD 114, and/or configured to receive a pattern loadedinto DMD 114 from DMD 114 or another device. Reconstructing the sequenceimages with a CUSP reconstruction algorithm may be an under-sampledinverse problem.

As previously noted, camera 112 captures u-View (a time-unshearedspectrum-undispersed image) and streak camera 116 captures s-View (atime-sheared spectrally-dispersed spatially-encoded image). The measuredoptical energy distributions in these two views are denoted as E_(u) andE_(s), respectively. Mathematically, they can be linked to the intensitydistribution of the dynamic scene I(x, y, t, λ) by

$\begin{matrix}{{\begin{bmatrix}{E_{u}\left( {x_{u},y_{u}} \right)} \\{E_{s}\left( {x_{s},y_{s}} \right)}\end{bmatrix} = {\begin{bmatrix}{{TQ}_{u}F_{u}} \\{\alpha\;{TS}_{t}Q_{s}S_{\lambda}{DF}_{s}C}\end{bmatrix}{I\left( {x,y,t,\lambda} \right)}}},} & (3)\end{matrix}$where C represents the spatial encoding by the DMD; F_(u) and F_(s)represent the spatial low-pass filtering due to the optics of CUSPimaging system 100 in u-View and s-View, respectively; D representsimage distortion in s-View with respect to the u-View; S_(λ) representsthe spectral dispersion in the horizontal direction due to diffractiongrating 118; Q_(u) and Q_(s) denote the quantum efficiencies of thecamera 112 and the photocathode of the streak camera 116, respectively;S_(t) represents the temporal shearing in the vertical direction withinstreak camera 116; T represents spatiotemporal-spectrotemporalintegration over the exposure time of the camera 112 and the streakcamera; and a denotes the experimentally calibrated energy ratio betweenthe streak camera 116 and camera 112. The dynamic scenes observed byboth active CUSP and passive CUSP are generalized herein as I(x, y, t,λ) for simplicity. Equation (3) can be modified to the followingconcatenated form E=O1(x, y, t, λ), where E=[E_(u),αE_(s)] and O standsfor the joint operator.

Given the operator O and the spatiotemporal-spectrotemporal sparsity ofthe dynamic scene, I(x, y, t, λ) can be recovered by solving thefollowing inverse problem:

$\begin{matrix}{\hat{I} = {{argmin}_{I}{\left\{ {{\frac{1}{2}{{E - {OI}}}_{2}^{2}} + {{\beta\Phi}(I)}} \right\}.}}} & (4)\end{matrix}$

In Equation (4), ∥⋅∥₂ denotes the l₂ norm. The first term denotes thediscrepancy between the solution I and the measurement E via theoperator O. The second term enforces sparsity in the domain defined bythe following regularizer Φ(I) while the regularization parameter βbalances these two terms. In some configuration, total variation (TV) isused in the four-dimensional x-y-t-λ, space as a regularizer. Toaccurately and stably reconstruct the dynamic scene, E is sent into asoftware program adapted from the two-step iterativeshrinkage/thresholding (TwIST) algorithm.

In the TwIST algorithm, the regularization parameter β was assignedvalues of 0.6, 0.5 and 1.0 for the three sets of experiments shown inFIGS. 2, 3, and 4 , respectively. Additionally, the maximum number ofiterations was set to 50. These are merely examples and other values mayalso be suitable. The total variation defined by equation (5) wasselected as the regularizer,

$\begin{matrix}{{\Phi(I)} = {{\Phi_{TV}(I)} = {{\sum\limits_{k}{\sum\limits_{q}{\sum\limits_{m,n}\sqrt{\left( {{I\left\lbrack {m,{n + 1},k,q} \right\rbrack} - {I\left\lbrack {m,n,k,q} \right\rbrack}} \right)^{2} + \left( {{I\left\lbrack {{m + 1},n,k,q} \right\rbrack} - {I\left\lbrack {m,n,k,q} \right\rbrack}} \right)^{2}}}}} + {\sum\limits_{m}{\sum\limits_{n}{\sum\limits_{k,q}{\sqrt{\left( {{I\left\lbrack {m,n,{k + 1},q} \right\rbrack} - {I\left\lbrack {m,n,k,q} \right\rbrack}} \right)^{2} + \left( {{I\left\lbrack {m,n,k,{q + 1}} \right\rbrack} - {I\left\lbrack {m,n,k,q} \right\rbrack}} \right)^{2}}.}}}}}}} & (5)\end{matrix}$

To implement the CUSP reconstruction, accurate estimations and/ormeasurements may be needed for the spatial low-pass filtering operatorsF_(u) and F_(s), the encoding matrix C[m, n], the distortion matrix D,and the adjoint of operator O. Discussion of how to estimate and/ormeasure the distortion matrix D is presented in U.S. Provisional PatentApplication No. 62/904,442, titled “Compressed-Sensing UltrafastSpectral Photography (CUSP)” and filed on Sep. 23, 2019, which has beenand is again hereby incorporated by reference in its entirety and forall purposes. An example of how to estimate and/or measure the otheroperators is described by J. Liang, C. Ma, L. Zhu, Y. Chen, L. Gao, andL. V. Wang, “Single-shot real-time video recording of a photonic Machcone induced by a scattered light pulse,” Science Advances 3, e1601814(2017), which is hereby incorporated by reference in its entirety.

CUSP's reconstruction of a data matrix of dimensions N_(x)×N_(y)×N_(ta)(active mode) or N_(x)×N_(y)×N_(tp)×N_(λ) (passive mode) may require a2D image of N_(x)×N_(y) in u-View and a 2D image of N_(col)×N_(row) ins-View. In one example of the active mode, N_(col)=N_(x)+(N_(ta)/P)−1and N_(row)=N_(y)+(vt_(sp)/d)(P−1); in one example of the passive mode,N_(col)=N_(x)+N_(λ)−1 and N_(row)=N_(y)+N_(tp)−1. The finite pixelcounts of streak camera 116 (e.g., 672×512 after 2×2 binning in oneconfiguration) may physically restrict N_(col)<672 and N_(row)<512. Inactive CUSP imaging, further described in connection with FIG. 2 , a rawstreak camera image of 609×430 pixels may be required to reconstruct adata matrix of N_(x)×N_(y)×N_(ta)=470×350×700. Similarly, in connectionwith the example of FIG. 3 , reconstruction of a data matrix ofN_(x)×N_(y)×N_(ta)=330×90×980 may require an image of 469×210 pixelsfrom the streak camera 116. In the passive-mode imaging example shown inFIG. 4 , an SR-FLIM data matrix ofN_(x)×N_(y)×N_(tp)×N_(λ)=110×110×400×100 may be associated with a streakcamera image of 209×509 pixels.

D. Streak Camera

FIG. 5 is a diagram of a streak camera such as streak camera 116 thatmay be utilized in a CUSP imaging system such as imaging system 100 ofFIG. 1 . As shown in FIG. 4 , streak camera 500 may include afully-opened, or partially-opened slit 502 (to enable 2D imaging), inputoptics 504, streak tube 506, and an internal camera 520 (e.g., a CCD,CMOS, or other 2D imaging sensor). The streak tube 506 may includephotocathode 508, accelerating mesh 510, sweep electrodes 512 (acrosswhich a sweeping voltage can be applied), microchannel plate 514 (whichamplifies the electron current via generation of secondary electrons),phosphor screen 516, and output optics 518, as examples. When operatingin focus mode, no sweeping voltage is applied to sweep electrodes 512.The dots between the sweep electrodes 512 in FIG. 5 representaccelerated electrons having different times of arrival and thusdifferent amounts of deflection by sweep electrodes 512. With the streakcamera utilized in the present configurations, the highest sweepingspeed is 100 fs per pixel, equivalent to 10 THz.

In at least some configurations, the spectral sensitivity of the streakcamera is taken into account in data acquisition and imagereconstruction. The measured quantum efficiency Q_(s)(λ) of thephotocathode 508—the photon-sensitive element in the streak tube 506—isplotted in graph a of FIG. 6 . Note that the output optics 518 and theinput optics 504 of the streak camera 500 may, in some configurations,be assumed to have uniform transmission within each band. Sincephotoelectrons lose their wavelength fingerprints after generation andacceleration, the spectral sensitivity of phosphor screen 516 andinternal camera 520 can be excluded.

A space-charge effect can occur when too many photoelectrons, confinedat the focus of an electron imaging system, repel each other, limitingboth spatial and temporal resolutions of the streak camera 500. Thespace-charge induced spread in the orthogonal directions was studied atdifferent optical intensities deposited at the entrance. A femtosecondlaser with a 1-kHz pulse repetition rate was used as the source. Spreadin the vertical direction y_(s) was equivalent to the spread in the timedomain. As shown in graph b of FIG. 6 , at low intensity, thespace-charge effect is negligible, but it becomes evident andintolerable quickly as the incident intensity increases. In practice, itis critical to control the incident intensity to reduce and/or minimizethe space-charge effect (e.g., to be less than 2 pixels). On the otherhand, the intensity has to be high enough to provide a desirablesignal-to-noise ratio (SNR). Thus, the intensity may need to adjusted tobalance between excessive space-charge effect and a sufficiently highsignal-to-noise ratio.

The data acquisition model of CUSP may presume that the streak camera500 responds linearly to the incident light intensity. Graph c of FIG. 6plots the measured response curve, which exhibits good linearity(>0.999) between the sensor pixel value and the incident lightintensity, at least for light intensities lower than where thespace-charge effect becomes evident.

The streak camera used in the present examples had a tested sweepinglinearity (i.e. linearity of the ultrafast sweeping voltage appliedinside the streak tube better than 0.996, which is sufficient. Inaddition, at a 10 THz sweeping speed and low light intensity, the streakcamera used in the present examples had a tested temporal resolution of230 fs. However, this value is for 1D ultrafast imaging only. At lowlight levels (e.g., 1000 photons per pixel in the streak camera's rawimage), the SNR may be too poor to produce clear CUSP images in a singleshot. At higher light levels (e.g., 20,000 photons per pixel in thestreak camera's raw image) that have a moderate SNR, the temporalresolution is typically larger than 400 fs. The temporal resolution ofactive CUSP is not bounded by these limits.

III. CUSP Active Mode Imaging of an Ultrafast Linear Optical Phenomenon

As shown in FIG. 2 , CUSP imaging system 100, configured in active mode(e.g., utilizing the illumination section 104), was used in imaging anultrafast linear optical phenomenon.

Simultaneous characterization of an ultrashort light pulse spatially,temporally, and spectrally may be useful, as examples, for studies onlaser dynamics and multimode fibers. As shown in schematic a of FIG. 2 ,a spatially and temporally chirped pulse was created by a pair by pairof gratings G1 and G2 (located in the optical path between glass rod 124and the scene 106). The first grating G1 may impart angular dispersioninto the light pulse, while the second grating G2 may remove thatangular dispersion such that the light is again collimated, but with anew spatial dispersion. Negative and positive temporal chirps from a270-mm-long glass rod and the grating pair G1 and G2, respectively, werecarefully balanced so that the combined temporal spread t_(d) was closeto the sub-pulse separation t_(sp)=2 ps. The pulse train irradiated asample of printed letters, which is used as the dynamic scene 106 (whoselocation is illustrated in FIG. 1 ). Exemplary frames from the CUSPreconstruction are summarized in part b of FIG. 2 . These frames showthat each sub-pulse swiftly sweeps across the letters from left toright. Due to spatial chirping by the grating pair G1 and G2, theillumination wavelength also changes from short to long over time. Inparticular, the frames at the start of a given sub-pulse have relativelyshort wavelengths (near the 785 nm lower range), while frames at the endof a given sub-pulse have relatively long wavelengths (near the 823 nmupper range). The normalized light intensity at a selected spatialpoint, plotted in graph c of FIG. 2 , contains five peaks, representingthe five sub-pulses. The peaks have an average full width at halfmaximum (FWHM) of 240 fs, corresponding to 4.5 nm in the spectrumdomain. Fourier transforming the intensity in the spectrum domain to thetime domain gives a pulse with a FWHM of 207 fs, indicating that oursystem operates at the optimal condition bounded by the time-bandwidthlimit.

Using a dispersion parametery μ=23.5 μm/nm, a chirp parameter η=52.6fs/nm and a pixel size d=6.45 μm, the active mode CUSP system 100 offersa frame rate as high as 70 Tfps. As examples, the active mode CUSPsystem 100 may have a frame rate greater than 10 Tfps, greater than 20Tfps, greater than 30 Tfps, greater than 40 Tfps, greater than 50 Tfps,greater than 60 Tfps, or greater than 70 Tfps. Simultaneously with suchframerates, the active mode CUSP system 100 may have a sequence depth ofat least 100 frames, at least 200 frames, at least 300 frames, at least400 frames, at least 500 frames, at least 600 frames, at least 700frames, at least 800 frames, at least 900 frames, or at least 1,000frames. A control experiment imaged the same scene using atrillion-frame-per-second CUP (T-CUP) technique with 10 Tfps. Itsreconstructed intensity evolution at the same point exhibits a temporalspread 3.2× wider than that of CUSP. In addition, within any timewindow, CUSP achieves an approximately 7× increase in the number offrames compared with T-CUP (see the inset of graph c of FIG. 2 ). Thus,CUSP dramatically surpasses the currently fastest single-shot imagingmodality in terms of both temporal resolution and sequence depth. Graphd of FIG. 2 plots the reconstructed total light intensities of the fivesub-pulses versus the illumination wavelength. Their profiles are closeto the ground truth measured by a spectrometer (labeled “Ref” in graphd).

Schematic a of FIG. 10 provides another illustration of the grating pairG1 and G2 used in the imaging of an ultrafast linear optical phenomenon.Graph b of FIG. 10 shows the spatial chirp, measured by a fiber-coupledspectrometer. The solid line gives the peak wavelength of the measuredspectrum as the spectrometer moves in the x direction, which matchedclosely with the theoretical prediction (the dashed-dotted line). Threeexemplary spectrometer measurements are plotted in solid lines. Graph cof FIG. 10 shows the temporal chirp, as measured by direct streak cameraimaging at 10 THz, with a test object formed from a 1D narrow slit inthe x direction. Theoretical estimation is plotted in solid line. Withinthe bandwidth for imaging (785 nm to 823 nm), a positive chirp of 7.7 pswas measured.

IV. CUSP Active Mode Imaging of an Ultrafast Non-Linear OpticalPhenomenon

As shown in FIG. 3 , CUSP imaging system 100, configured in active mode(e.g., utilizing the illumination section 104), was used in imaging anultrafast non-linear optical phenomenon.

Nonlinear light-matter interactions are indispensable in opticalcommunications and quantum optics, among other fields. An example of anonlinear light-matter interaction of interest is optical-field-inducedbirefringence, a result of a third-order nonlinearity. As shown inschematic a of FIG. 3 , a single 48-fs laser pulse (referred to as the‘gate’ pulse), centered at 800 nm and linearly polarized along the ydirection, is focused into a Bi₄Ge₃O₁₂ (BGO) slab to induce transientbirefringence. A second beam (referred to as the ‘detection’ pulse)—atemporally chirped pulse train from the illumination section 104 of theCUSP system 100—was focused on the slab from an orthogonal direction,going through a pair of linear polarizers P1 and P2 that sandwich theBGO. This is a Kerr gate setup since the two polarizers havepolarization axes aligned at +45° and −45°, respectively. The Kerr gatehas a finite transmittance of T_(Kerr)=(1−cos φ)/2 only where the gatepulse travels. Here, φ, proportional to the gate pulse intensity,represents the gate-induced phase delay between the two orthogonalpolarization directions x and y.

The CUSP imaging system 100 imaged the gate pulse, with a peak powerdensity of 5.6×10¹⁴ mW/cm² at its focus, propagating in the BGO slab. Inthe first and second experiments (graphs b and c of FIG. 3 ,respectively), the gate focus was outside and inside the field of view(FOV), respectively. Graphs b and c of FIG. 3 contain 3D visualizationsof the reconstructed dynamics. Select frames from the reconstruction ofthe first experiment are shown in sequence d of FIG. 3 (the selectedframes are outlined and identified in graph b). Select frames from thereconstruction of the second experiment are shown in sequence e of FIG.3 (the selected frames are outlined and identified in graph c). As thegate pulse travels and focuses, the accumulated phase delay φ increases,therefore T_(Kerr) becomes larger. The centroid positions of the gatepulse (i.e. the transmission region in the Kerr medium) along thehorizontal axis x versus time t are plotted at the bottom of graphs band c, matching well with the theoretical estimation based on arefractive index of 2.62. Seven sub-pulses were included in theillumination to provide a 14-ps-long observation window and capture atotal of 980 frames.

Re-distribution of electronic charges in BGO lattices driven by anintense light pulse, like in other solids, serves as the dominantmechanism underlying the transient birefringence, which is much fasterthan re-orientation of anisotropic molecules in liquids, such as carbondisulfide. To study this ultrafast process, one spatial location fromsequence d of FIG. 3 was chosen to show its locally normalizedtransmittance evolution, which is plotted in graph f of FIG. 3 . ItsFWHM of 455 fs is close to the relaxation time of BGO reported in theliterature.

In stark contrast with the pump-probe method, CUSP requires only onesingle laser pulse to observe the entire time course of its interactionwith the material in 2D space. As discussed below, the Kerr gate in ourexperiment was designed to be highly sensitive to random fluctuations inthe gate pulse intensity. The pump-probe measurements thus flickerconspicuously, due to shot-to-shot variations, while CUSP exhibits asmooth transmittance evolution, owing to single-shot acquisition. Asdiscussed below in connection with FIG. 12 , the fractional fluctuationin intensity is amplified 11 times in transmittance.

A detailed schematic of the Kerr gate setup is shown in FIG. 11 . Asshown in FIG. 11 , original 48-fs pulse is horizontally polarized (x).It is split into the gate and detection arms by a beam splitter 1302having a low or minimal group velocity dispersion (GVD).

In the gate arm, a hollow-roof prism mirror (HRPM) may be mounted on ahigh-precision motorized stage (that translates the HRPM along the“optical delay line”) having a 300 nm step size (equivalently 2 fs intime delay). By moving the HRPM, the time delay between the gate anddetection arms can be tuned. A half-wave-plate (HWP1) rotates thepolarization to vertical (y). Two cylindrical lenses (CyL1 and CyL2) ofdifferent focal lengths reshape the round beam into an elliptical formand focus it into the BGO crystal. The short-focal-length lens (CyL2)may have motion control along the x direction to move the focal spot inand out of the field of view. In the detection arm, which was coupledwith the illumination section 104 of the active CUSP system 100, thebeam size is firstly shrunk by 2 times by a beam de-expander. Anotherhalf-wave-plate (HWP2) aligns the polarization angle of the detectionlight to that of the first polarizer's (P1) polarization axis. An N-SF11rod of 95-mm long with a chirp parameter of η=η_(rod_2)=−52.7 fs/nm wasdeployed for 70-Tfps imaging.

BGO is known for producing multi-photon-absorption induced fluorescence(MPF) since its 4.8 eV bandgap is close to the three-photon energy ofthe 800 nm light. We used a long-pass filter (LPF) to eliminate thisundesired fluorescence. The measured spectrum shown in graph 1304 ofFIG. 11 proves that the long-pass filter with 715 nm cut-off caneffectively block the MPF.

The Kerr effect introduces transient birefringence inside the medium(BGO crystal). In other words, the refractive index along thepolarization direction of the gate light (y) is changed linearlyproportionally to the gate pulse intensity,Δn=κ|{right arrow over (E)} _(gate)|² =κI _(gate).  (6)

The nonlinearity coefficient K is proportional to the third-ordersusceptibility χ⁽³⁾. As a result, the detection light accumulatesdifferent phases between two orthogonal polarizations where it meets thegate pulse in the BGO. Since P2's and P1's polarization axes areorthogonal to each other in the Kerr gate setup, the transmittance ofthe Kerr gate is

$\begin{matrix}{T_{\bot} = {T_{Kerr} = {\frac{1 - {\cos\varphi}}{2}.}}} & (7)\end{matrix}$

Here, φ=k_(BGO)Δnl_(Kerr), in which k_(BGO) is the angular wavenumber inBGO, and l_(Kerr) is the interaction length between the gate pulse andthe detection pulse. When the detection light meets the traveling gatepulse, φ has a finite value, leading to high transmittance. When thedetection misses the gate, φ=0, displaying a dark background T_(⊥)=0.

In order to measure the phase retardation φ, P2 was rotated to bealigned with P1. In this case, the transmittance after P2 becomes

$\begin{matrix}{T_{} = {\frac{1 + {\cos\varphi}}{2}.}} & (8)\end{matrix}$

φ=π/9 was computed near the focus of the gate pulse with a peak powerdensity of 5.6×10¹⁴ mW/cm².

Taking the derivative of Equation (7) and considering that φ isproportional to I_(gate), we obtain the following relation:

$\begin{matrix}{\frac{{dT}_{Kerr}}{T_{Kerr}} = {\frac{\varphi\sin\varphi}{1 - {\cos\varphi}} \cdot {\frac{{dI}_{gate}}{I_{gate}}.}}} & (9)\end{matrix}$

Therefore, the fractional change of the Kerr gate transmittance isproportional to the fractional change of the gate pulse intensity. Wedefine coefficient A=(φ sin φ)/(1−cos φ), which is plotted in graph a ofFIG. 12 . In our Kerr gate, the phase retardation φ ranges from 0 toπ/9, where the transmittance is sensitive to random fluctuations in thegate pulse intensity.

In the experimental study, a total of 200 consecutive shots werecaptured while the time delay between the gate pulse and the detectionpulse was fixed. Here, a single 48-fs pulse was used as the detectionpulse. The transmittance profile varied dramatically with a relativechange of 0.175 (standard deviation/mean, or SD/M for short) as shown ingraph c of FIG. 12 . A set of reference images were also taken when thegate pulse was blocked and the polarizers P1 and P2 were set parallel.These reference images directly measure the laser intensity fluctuation,showing a relative change of only 0.016. As shown in chart c of FIG. 12, the Kerr gate transmittance has SD/M 11 times as large as that of thereference intensity.

Such a high sensitivity to random fluctuations calls for single-shotultrafast imaging, and conventional pump-probe imaging may not beapplicable. Compared with CUSP and T-CUP, the pump-probe method displaysa much noisier transmittance evolution. In a pump-probe measurement, oneimage is acquired for a preset time delay. Therefore, 980 independentacquisitions were used to observe the entire dynamics in graph b of FIG.3 . Since the fractional intensity fluctuation is 11 times greater thanin CUSP, averaging over 121 images per time delay is required tocompensate for the fluctuation. Therefore, pump-probe imaging needs >10⁵laser shots to acquire the dynamics with the same stability and sequencedepth as CUSP. In other words, CUSP outperforms pump-probe imaging by>10⁵ times in data acquisition throughput.

FIG. 12 also illustrates, in graph a, coefficient A connecting thefractional change of the gate pulse intensity to that of the Kerr gatetransmittance. Image sequence b and graphs c and d show a study on thestability of the stability of the Kerr gate. In particular, imagesequence b includes representative shots of the Kerr gate transmittanceprofile at a fixed time delay. Graph c shows relative change (standarddeviation/mean) of the intensity from the reference experiment and thatof the transmittance from the Kerr gate experiment, at five spatialpoints labelled in shot 15 of sequence b. Graph d shows sequences ofintensity and transmittance from point 3, normalized to their meanvalues.

V. CUSP Passive Mode Imaging of an Ultrafast Fluorescence Phenomenon

In passive mode, CUSP provides four-dimensional (4D) spectral imaging at0.5×10¹² fps, allowing the first single-shot spectrally resolvedfluorescence lifetime imaging microscopy (SR-FLIM). As examples, thepassive mode CUSP system may have a frame rate greater than 1×10¹¹ fps,greater than 2×10¹¹ fps, greater than 3×10¹¹ fps, greater than 4×10¹¹fps, greater than or 5×10¹¹ fps (i.e., 0.5×10¹² fps, or 0.5 Tfps).Simultaneously with such framerates, the passive mode CUSP system mayhave a sequence depth of at least 100 frames, at least 200 frames, atleast 300 frames, at least 400 frames, at least 500 frames, at least 600frames, at least 700 frames, at least 800 frames, at least 900 frames,or at least 1,000 frames.

Both the emission spectrum and fluorescence lifetime are importantproperties of molecules, which have been exploited by biologists andmaterial scientists to investigate a variety of biological processes andmaterial characteristics. Over the past decades, time-correlated singlephoton counting (TCSPC) has been the gold-standard tool for SR-FLIM.Nonetheless, TCSPC typically takes tens of milliseconds to even secondsto acquire one dataset, since it depends on repeated measurements.

A schematic of a passive CUSP system configured for SR-FLIM is shown indiagram a of FIG. 4 . The configuration includes a fluorescencemicroscope that interfaces with the imaging section 102 of the CUSPsystem 100. The system may also include a dichroic mirror (DM), along-pass emission filter (EmF), a short-pass excitation filter (ExF),and other suitable optics. The dichroic mirror and the long-pass filter(EmF) effective blocked stray excitation light from passing to theimaging section 102 of the CUSP system 100.

The SR-FLIM system implemented with CUSP provides a spectral resolutionof 13 nm over the 200-nm bandwidth. A single 532-nm picosecond pulse wasdeployed to excite fluorescence from a sample of Rhodamine 6G dye (Rh6G)in methanol. The Rh6G solution was masked by a negative USAF target,placed at the sample plane. Three Rh6G concentrations (22 mM, 36 mM and40 mM) with three different spatial patterns were imaged andreconstructed at 0.5 Tfps. The final data contains N_(tp)=400 framesover an exposure time of 0.8 ns, and N_(λ)=100 wavelength samples.Fluorescence lifetime can be readily extracted by single-exponentialfitting. 3D graphs b, c, and d of FIG. 4 illustrate the spatio-spectraldistributions of the fluorescence lifetimes. Rh6G with a higherconcentration has a shorter lifetime due to increased pathways fornon-radiative relaxation. The spatial intensity distributions (insets ofgraphs b, c, and d) show well-preserved spatial resolutions. Graph e ofFIG. 4 plots the intensity distribution of the 22-mM sample in the t−λ,space, clearly revealing that the emission peaks at ˜570 nm and decaysrapidly after excitation. We show in graph f that lifetimes remainrelatively constant over the entire emission spectra and exhibit minutevariations over the spatial domain. The grey bands in graph f representthe standard deviations of lifetimes in the spatial domain. Theseuniform spatial distributions are also confirmed by the spectrallyaveraged lifetime maps in graph g of FIG. 4 .

A schematic of the entire passive CUSP system for SR-FLIM is shown inFIG. 13 . Fluorescence of short lifetimes is known to have low quantumefficiency. Therefore, it is useful to make use of all the emittedphotons. The system shown in FIG. 13 differs from that of FIG. 1 , inthat the DMD is placed in retro-reflection, where the DMD is tilted by12°. Each mirror in the DMD is configurable between a +12° (“ON”) or−12° (“OFF”) state, relative to the DMD's surface normal. In thismodified system, two separate sets of optical lenses were used toproject the image onto the DMD and then relay the encoded image from theDMD to the streak camera, respectively. The 50/50 (R/T) beam splitter ofFIG. 1 was also replaced by beam splitter with a 90% reflectance and a10% transmittance (to send more light towards the DMD). These changesharnesses 3.6×photons in s-View, compared with that in the FIG. 1configuration. Similar to the active CUSP system, a diffraction gratingof period Λ_(FLIM)=1.667 μm was inserted at a distance l_(FLIM)=14 mmfrom the entrance port of the streak camera (as shown in image a of FIG.13 ).

VI. Data Acquisition

A. Passive Mode

FIG. 11 illustrates an example of one potential data acquisition processof a CUSP system, although other processes may be suitable for CUSPimaging. To simplify the explicit expressions for both u-View ands-View, we make the following assumptions, without loss of generality.First, the entire imaging system 100 has a magnification of 1×. Second,the DMD 114, the external camera 112, and the internal camera of thestreak camera 116 have the same pixel size, denoted as d, and theirpixels are matched. Third, the scene is perfectly imaged to the DMD 114.To simplify the notations, we choose a voxel of (d, d, τ, δ), in thex-y-t-λ, space, where τ=d/v and δ=d/|μ|. Here v is the temporal shearingspeed of the streak camera and μ is the spectral dispersion parameter.

In u-View, the dynamic scene I(x, y, t, λ) (scene 106 of FIG. 1 ) isimaged on the external camera 114 through both low-pass filtering causedby the optical components, denoted as F_(u), andspatiotemporal-spectrotemporal integration, denoted as T,

$\begin{matrix}{{{I_{F_{u}}\left( {x_{u},y_{u},t,\lambda} \right)} = {F_{u}\left\{ {I\left( {x,y,t,\lambda} \right)} \right\}}},} & (10)\end{matrix}$ $\begin{matrix}{{E_{u}\left\lbrack {m,n} \right\rbrack} = {{T\left\{ {{Q_{u}(\lambda)} \cdot {I_{F_{u}}\left( {x_{u},y_{u},t,\lambda} \right)}} \right\}} = {\int{{dx}_{u}{\int{{dy}_{u}{\left\{ {\left\lbrack {\int{{dt}{\int{d\lambda{{Q_{u}(\lambda)} \cdot {I_{F_{u}}\left( {x_{u},y_{u},t,\lambda} \right)}}}}}} \right\rbrack \cdot {{rect}\left\lbrack {{\frac{x_{u}}{d} - \left( {m + \frac{1}{2}} \right)},{\frac{y_{u}}{d} - \left( {n + \frac{1}{2}} \right)}} \right\rbrack}} \right\}.}}}}}}} & (11)\end{matrix}$

In equation (10), x_(u) and y_(u) are the spatial coordinates of theexternal camera 112. In Equation (11), E_(u)[m, n] represents theoptical energy measured by the [m, n] pixel on the camera 112, andQ_(u)(λ) is the quantum efficiency of the external camera 112.

In s-View, we firstly apply spatial encoding to I(x, y, t, λ) by apseudo-random binary pattern C(x,y) displayed on the DMD 114, giving thefollowing intensity distribution:I _(C)(x,y,t,λ)=C(x,y)I(x,y,t,λ).  (12)

The encoded scene is then relayed to the entrance port of the streakcamera 116 by passing through the imaging system (e.g., the opticalcomponents within imaging section 102), which also introduces spatiallow-pass filtering F_(s):I _(F) _(s) (x,y,t,λ)=F _(s) {I _(C)(x,y,t,λ)}.  (13)

Next, an image distortion operator of the s-View is applied:I _(D)(x,y,t,λ)=D{I _(F) _(s) (x,y,t,λ)}.  (14)

In the next step, the dynamic scene is spectrally dispersed by thediffraction grating 118 of FIG. 1 . Here, we define an intermediatecoordinate system right at the entrance port of the streak camera 116:x′=x+μ(λ−λ₀), y′=y. Hence, the dispersed image I_(S) _(λ) is given byI _(S) _(λ) (x′,y′,t,λ)=S _(λ) {I _(D)(x,y,t,λ)}=I_(D)(x′−μ(λ−λ₀),y′,t,λ).  (15)

Afterward, the dispersed scene is captured by the streak camera 116.Here, the quantum efficiency Q_(s)(λ) of the streak camera photocathode516 of FIG. 5 kicks in so that the generated photoelectron energy isI _(phe)(x′,y′,t,λ)=Q _(s)(λ)·I _(S) _(λ) (x′,y′,t,λ).  (16)

Here, the subscript “phe” stands for “photoelectrons”. We define thespatial axes of the streak camera 116 as x_(s)=x′ and y_(s)=y′+vt. Thus,the temporal shearing along the vertical spatial axis can be expressedbyI _(S) _(t) (x _(s) ,y _(s) ,t,λ)=S _(t) {I _(phe)(x′,y′,t,λ)}=Q_(s)(λ)·I _(S) _(λ) (x _(s) ,y _(s) −vt,t,λ).  (17)

Finally, I_(S) _(t) (x_(s), y_(s), t, λ) is imaged to an internal sensor520 of FIG. 5 by spatiotemporal-spectrotemporal integration T. Akin tothe u-View, the optical energy measured by the [m, n] pixel on thesensor 520 takes the form

$\begin{matrix}{{E_{s}\left\lbrack {m,n} \right\rbrack} = {{T\left\{ {I_{S_{t}}\left( {x_{s},y_{s},t,\lambda} \right)} \right\}} = {\int{{dx}{\int{{dy}\left\{ {{\left\lbrack {\int{{dt}{I_{S_{t}}\left( {x_{s},y_{s},t,\lambda} \right)}}} \right\rbrack \cdot {rect}}{\left. \left\lbrack {{\frac{x_{s}}{d} - \left( {m + \frac{1}{2}} \right)},{\frac{y_{s}}{d} - \left( {n + \frac{1}{2}} \right)}} \right\rbrack \right\}.}} \right.}}}}}} & (18)\end{matrix}$

Taking Equations (15)-(17) into (18), we get

$\begin{matrix}{{E_{s}\left\lbrack {m,n} \right\rbrack} = {\int{{dx}{\int{{dy}{\left\{ {\left\lbrack {\int{{dt}{\int{d\lambda{{Q_{s}(\lambda)} \cdot {I_{D}\left( {{x_{s} - {\mu\left( {\lambda - \lambda_{0}} \right)}},{y_{s} - {vt}},t,\lambda} \right)}}}}}} \right\rbrack \cdot {{rect}\left\lbrack {{\frac{x_{s}}{d} - \left( {m + \frac{1}{2}} \right)},{\frac{y_{s}}{d} - \left( {n + \frac{1}{2}} \right)}} \right\rbrack}} \right\}.}}}}}} & (19)\end{matrix}$

The image pixel value that is read out from the streak camera 116 islinearly proportional to the deposited optical energy E_(s) (see, e.g.graph c of FIG. 6 ).

To use this model in a compressed sensing-based reconstructionalgorithm, it is helpful to derive a discrete-to-discrete model bydiscretizing the dynamic scene:

$\begin{matrix}{{I\left\lbrack {m,n,k,q} \right\rbrack} = {\int{d\lambda{\int{{dt}{\int{{dx}{\int{{dy}{{I\left( {x,y,t,\lambda} \right)} \cdot {{{rect}\left\lbrack {{\frac{x}{d} - \left( {m + \frac{1}{2}} \right)},{\frac{y}{d} - \left( {n + \frac{1}{2}} \right)},{\frac{t}{\tau} - \left( {k + \frac{1}{2}} \right)},{\frac{\lambda - \lambda_{0}}{\delta} - \left( {q + \frac{1}{2}} \right)}} \right\rbrack}.}}}}}}}}}}} & (20)\end{matrix}$

In Equation (20), m, n, k, q are non-negative integers. Therefore, themeasurement of the u-View can be approximated by

$\begin{matrix}{{E_{u}\left\lbrack {m,n} \right\rbrack} = {\frac{d^{4}}{v{❘\mu ❘}}{\sum\limits_{k}{\sum\limits_{q}{{Q_{u}\lbrack q\rbrack} \cdot {{\left( {h_{u}*I} \right)\left\lbrack {m,n,k,q} \right\rbrack}.}}}}}} & (21)\end{matrix}$

Here, h_(u) is the discrete convolution kernel of the operator F_(u),and * stands for the discrete 2D spatial convolution operation.

For the s-View, the encoding mask is discretized to

$\begin{matrix}{{C\left\lbrack {m,n} \right\rbrack} = {\int{{dx}{\int{{dy}{{C\left( {x,y} \right)} \cdot {{{rect}\left\lbrack {{\frac{x}{d} - \left( {m + \frac{1}{2}} \right)},{\frac{y}{d} - \left( {n + \frac{1}{2}} \right)}} \right\rbrack}.}}}}}}} & (22)\end{matrix}$

Then, the encoded scene becomesI _(C)[m,n,k,q]=C[m,n]·I[m,n,k,q].  (23)

Eventually, the discretized form of the streak camera measurement isrepresented by

$\begin{matrix}{{{E_{s}\left\lbrack {m,n} \right\rbrack} = {\frac{d^{4}}{v{❘\mu ❘}}{\sum\limits_{k}{\sum\limits_{q}{{Q_{s}\lbrack q\rbrack} \cdot {\left( {h_{s}*I_{C}} \right)\left\lbrack {{m_{D} - q},{n_{D} - k},k,q} \right\rbrack}}}}}},} & (24)\end{matrix}$where h_(s) is the discrete convolution kernel of the operator F_(s),m_(D) and n_(D) are the discrete coordinates transformed according tothe distortion operator D.

B. Active Mode

In the passive version of CUSP, time and spectrum are independent,therefore we can directly apply the general model derived above.However, in active mode, spectrum and time are dependent because we usethe spectrum for time stamping. Consequently, the general model shouldpreferable be modified. To start with, the dynamic scene, illuminated bya train of chirped pulses, can be expressed byI(x,y,t)=I(x,y,pt _(sp)+η(λ−λ₀))=I(x,y,t(p,λ)).  (25)

We can still use Equation (20) as its discrete form, however,k=round(pt_(sp)/τ) is a non-negative integer that is assigned to thesub-pulse sequence p only.

For the u-View, Equations (10) and (11) are replaced by

$\begin{matrix}{{{I_{F_{u}}\left( {x_{u},y_{u},{t\left( {p,\lambda} \right)}} \right)} = {F_{u}\left\{ {I\left( {x,y,{t\left( {p,\lambda} \right)}} \right)} \right\}}},} & (26)\end{matrix}$ $\begin{matrix}{{E_{u}\left\lbrack {m,n} \right\rbrack} = {{T\left\{ {{Q_{u}(\lambda)} \cdot {I_{F_{u}}\left( {x_{u},y_{u},{t\left( {p,\lambda} \right)}} \right)}} \right\}} = {\int{{dx}_{u}{\int{{dy}_{u}{\left\{ {\left\lbrack {\sum\limits_{p}{\int{d\lambda{{Q_{u}(\lambda)} \cdot {I_{F_{u}}\left( {x_{u},y_{u},{t\left( {p,\lambda} \right)}} \right)}}}}} \right\rbrack \cdot {{rect}\left\lbrack {{\frac{x_{u}}{d} - \left( {m + \frac{1}{2}} \right)},{\frac{y_{u}}{d} - \left( {n + \frac{1}{2}} \right)}} \right\rbrack}} \right\}.}}}}}}} & (27)\end{matrix}$

Therefore, the discrete-to-discrete model for this view can be adaptedfrom Equation (21):

$\begin{matrix}{{{E_{u}\left\lbrack {m,n} \right\rbrack} = {\frac{d^{4}}{v{❘\mu ❘}}{\sum\limits_{p}{\sum\limits_{q}{{Q_{u}\lbrack q\rbrack} \cdot {\left( {h_{u}*I} \right)\left\lbrack {m,n,{k(p)},q} \right\rbrack}}}}}},} & (28)\end{matrix}$where k=round(pt_(sp)/τ), p=0, 1, 2, . . . , (P−1), and q=0, 1, 2, . . ., ((N_(ta)/P)−1). N_(ta) is the number of recorded frames in the activemode.

For the s-View, we can basically follow the same derivation process fromEquation (12) to (15), but replace t by pt_(sp) and re-define thevertical axis of the streak camera as y_(s)=y′+v(pt_(sp)+η(λ−λ₀)). As aresult, the optical energy received by the internal CCD is

$\begin{matrix}{{E_{s}\left\lbrack {m,n} \right\rbrack} = {\int{{dx}{\int{{dy}{\left\{ {\left\lbrack {\sum\limits_{p}{\int{d\lambda{{Q_{u}(\lambda)} \cdot {I_{D}\left( {{x_{s} - {\mu\left( {\lambda - \lambda_{0}} \right)}},{y_{s} - {v\left( {{pt}_{sp} + {\eta\left( {\lambda - \lambda_{0}} \right)}} \right)}},{t\left( {p,\lambda} \right)}} \right)}}}}} \right\rbrack \cdot {{rect}\left\lbrack {{\frac{x_{s}}{d} - \left( {m + \frac{1}{2}} \right)},{\frac{y_{s}}{d} - \left( {n + \frac{1}{2}} \right)}} \right\rbrack}} \right\}.}}}}}} & (29)\end{matrix}$

Similarly, its discrete-to-discrete model is given by

$\begin{matrix}{{{E_{s}\left\lbrack {m,n} \right\rbrack} = {\frac{d^{4}}{v{❘\mu ❘}}{\sum\limits_{p}{\sum\limits_{q}{{Q_{s}\lbrack q\rbrack} \cdot {\left( {h_{s}*I_{C}} \right)\left\lbrack {{m_{D} - q},{n_{D} - {r\left( {p,q} \right)}},{k(p)},q} \right\rbrack}}}}}},{{{in}{which}r} = {{{round}\left\lbrack {\left( {{pt}_{sp} + {\eta\left( {\lambda - \lambda_{0}} \right)}} \right)/\tau} \right\rbrack} = {{round}\left\lbrack {\left( {{pt}_{sp} + {\eta q\delta}} \right)/\tau} \right\rbrack}}},{k = {{round}\left( {{pt}_{sp}/\tau} \right)}},{p = 0},1,2,\ldots,\left( {P - 1} \right),{{{and}q} = 0},1,2,\ldots,{\left( {\left( {N_{ta}/P} \right) - 1} \right).}} & (30)\end{matrix}$VII. Additional Considerations

Modifications, additions, or omissions may be made to any of theabove-described embodiments without departing from the scope of thedisclosure. Any of the embodiments described above may include more,fewer, or other features without departing from the scope of thedisclosure. Additionally, the steps of described features may beperformed in any suitable order without departing from the scope of thedisclosure. Also, one or more features from any embodiment may becombined with one or more features of any other embodiment withoutdeparting from the scope of the disclosure. The components of anyembodiment may be integrated or separated according to particular needswithout departing from the scope of the disclosure.

It should be understood that certain aspects described above can beimplemented in the form of logic using computer software in a modular orintegrated manner. Based on the disclosure and teachings providedherein, a person of ordinary skill in the art will know and appreciateother ways and/or methods to implement the present invention usinghardware and a combination of hardware and software.

Any of the software components or functions described in thisapplication, may be implemented as software code using any suitablecomputer language and/or computational software such as, for example,Java, C, C #, C++ or Python, LabVIEW, Mathematica, or other suitablelanguage/computational software, including low level code, includingcode written for field programmable gate arrays, for example in VHDL.The code may include software libraries for functions like dataacquisition and control, motion control, image acquisition and display,etc. Some or all of the code may also run on a personal computer, singleboard computer, embedded controller, microcontroller, digital signalprocessor, field programmable gate array and/or any combination thereofor any similar computation device and/or logic device(s). The softwarecode may be stored as a series of instructions, or commands on a CRMsuch as a random access memory (RAM), a read only memory (ROM), amagnetic medium such as a hard-drive or a floppy disk, or an opticalmedium such as a CD-ROM, or solid stage storage such as a solid statehard drive or removable flash memory device or any suitable storagedevice. Any such CRM may reside on or within a single computationalapparatus, and may be present on or within different computationalapparatuses within a system or network. Although the foregoing disclosedembodiments have been described in some detail to facilitateunderstanding, the described embodiments are to be consideredillustrative and not limiting. It will be apparent to one of ordinaryskill in the art that certain changes and modifications can be practicedwithin the scope of the appended claims.

The terms “comprise,” “have” and “include” are open-ended linking verbs.Any forms or tenses of one or more of these verbs, such as “comprises,”“comprising,” “has,” “having,” “includes” and “including,” are alsoopen-ended. For example, any method that “comprises,” “has” or“includes” one or more steps is not limited to possessing only those oneor more steps and can also cover other unlisted steps. Similarly, anycomposition or device that “comprises,” “has” or “includes” one or morefeatures is not limited to possessing only those one or more featuresand can cover other unlisted features.

All methods described herein can be performed in any suitable orderunless otherwise indicated herein or otherwise clearly contradicted bycontext. The use of any and all examples, or exemplary language (e.g.“such as”) provided with respect to certain embodiments herein isintended merely to better illuminate the present disclosure and does notpose a limitation on the scope of the present disclosure otherwiseclaimed. No language in the specification should be construed asindicating any non-claimed element essential to the practice of thepresent disclosure.

Groupings of alternative elements or embodiments of the presentdisclosure disclosed herein are not to be construed as limitations. Eachgroup member can be referred to and claimed individually or in anycombination with other members of the group or other elements foundherein. One or more members of a group can be included in, or deletedfrom, a group for reasons of convenience or patentability. When any suchinclusion or deletion occurs, the specification is herein deemed tocontain the group as modified thus fulfilling the written description ofall Markush groups used in the appended claims.

What is claimed is:
 1. A compressed-sensing ultrafast spectralphotography (CUSP) system for obtaining a series of final recordedimages of a subject, comprising: an illumination section comprising:first and second beam splitters configured to receive a first laserpulse and configured to convert the first laser pulse into a pulse trainthat comprises a plurality of sub-pulses evenly separated in time; andan optical component configured to temporally stretch and chirp each ofthe sub-pulses of the pulse train, wherein the illumination section isconfigured to illuminate an object of interest with thetemporally-stretched and chirped sub-pulses of the pulse train toproduce a first series of images; and an imaging section comprising: aspatial encoding module configured to receive the first series of imagesand to produce a second series of spatially-encoded images, eachspatially-encoded image of the second series comprising at least a firstview including one image of the first series superimposed with apseudo-random binary spatial pattern; and a streak camera coupled to thespatial encoding module, the streak camera configured to receive thesecond series of spatially-encoded images, to deflect eachspatially-encoded image by a temporal deflection distance that varies asa function of time-of-arrival, and to integrate the temporally-deflectedimages into a single raw CUSP image.
 2. The CUSP system of claim 1,further comprising: an additional optical element optically disposedbetween the spatial encoding module and the streak camera, wherein theadditional optical element is configured to spectrally disperse thesecond series of spatially-encoded images before images of the secondseries of spatially-encoded images are received by the streak camera. 3.The CUSP system of claim 2, wherein the streak camera is configured todeflect the second series of spatially-encoded images along a firstaxis, wherein the additional optical element is configured to spectrallydisperse the second series of spatially-encoded images along a secondaxis, and wherein the first axis is orthogonal to the second axis. 4.The CUSP system of claim 3, wherein the additional optical elementcomprises a diffracting grating.
 5. The CUSP system of claim 1, furthercomprising: a micrometer stage configured to adjust a spacing betweenthe first beam splitter relative to the second beam splitter with a stepsize no greater than 600 nm.
 6. The CUSP system of claim 1, wherein eachof the first and second beam splitters comprise a beam splitter coating,wherein the beam splitter coating of the first beam splitter is on asurface of the first beam splitter that faces the second beam splitter,and wherein the beam splitter coating of the second beam splitter is ona surface of the second beam splitter that faces the first beamsplitter.
 7. The CUSP system of claim 1, wherein the raw CUSP imagecomprises an image comprises a time-sheared spectrally-dispersedspatially-encoded image.
 8. The CUSP system of claim 1, furthercomprising: an additional beam splitter configured to divide the firstseries of images into first and second fractions, wherein the CUSPsystem is configured such that the first fraction is conveyed to thespatial encoding module; and an additional camera configured to receivethe second fraction of the first series of images, the additional cameraconfigured to temporally integrate the second fraction of the firstseries of images into an additional raw image.
 9. The CUSP system ofclaim 1, wherein the streak camera comprises an entrance slit configuredin a fully open position.
 10. A compressed-sensing ultrafast spectralphotography (CUSP) system for obtaining a series of final recordedimages of a subject, comprising: a spatial encoding module configured toreceive a first series of images and to produce a second series ofspatially-encoded images, each spatially-encoded image of the secondseries comprising at least a first view including one image of the firstseries superimposed with a pseudo-random binary spatial pattern; anoptical element configured to receive the second series ofspatially-encoded images and to produce a third series ofspatially-encoded and spectrally-dispersed images; and a streak cameraconfigured to receive the third series of spatially-encoded andspectrally-dispersed images, to deflect each spatially-encoded andspectrally-dispersed image by a temporal deflection distance that variesas a function of time-of-arrival, and to integrate thetemporally-deflected images into a single raw CUSP image.
 11. The CUSPsystem of claim 10, wherein the optical element comprises a diffractiongrating.
 12. The CUSP system of claim 10, wherein the spatial encodingmodule comprises a digital micromirror device comprising an array ofmicromirrors.
 13. The CUSP system of claim 10, further comprising: abeam splitter configured to divide the first series of images into firstand second fractions, wherein the CUSP system is configured such thatthe first fraction is conveyed to the spatial encoding module; and anadditional camera configured to receive the second fraction of the firstseries of images, the additional camera configured to temporallyintegrate the second fraction of the first series of images into anadditional raw image.
 14. A method of obtaining a series of finalrecorded images of an object using a compressed-sensing ultrafastspectral photography (CUSP) system, the method comprising: collecting afirst series of images of the object; superimposing a pseudo-randombinary spatial pattern onto each image of the first series to produce asecond series of spatially-encoded images; dispersing each image of thesecond series of spatially-encoded images by spectrum to produce a thirdseries of spatially-encoded and spectrally-dispersed images; deflectingeach spatially-encoded and spectrally-dispersed image of the thirdseries by a temporal deflection distance that varies as a function of atime-of-arrival of each spatially-encoded image to produce a fourthseries of time-sheared spatially-encoded, spectrally-dispersed images;integrating and recording the fourth series of time-shearedspatially-encoded spectrally-dispersed images as a single raw CUSPimage; and reconstructing a fifth series of final images by processingthe single raw CUSP image according to an image reconstructionalgorithm.
 15. The method of claim 14, wherein the reconstructed fifthseries of final images have a framerate of at least 40 trillion framesper second.
 16. The method of claim 14, wherein the reconstructed fifthseries of final images have a framerate of at least 70 trillion framesper second.
 17. The method of claim 14, wherein the reconstructed fifthseries of final images comprise single-shot spectrally resolved imagesat a framerate of at least 3×10¹¹ frames per second.
 18. The method ofclaim 14, further comprising: integrating and recording the first seriesof images as an additional raw image, wherein reconstructing the fifthseries of final images by processing the single raw CUSP image accordingto the image reconstruction algorithm comprises processing the singleraw CUSP image and the additional raw image according to the imagereconstruction algorithm.
 19. The method of claim 14, further comprisingilluminating the object with a plurality of temporally-chirped laserpulses to create the first series of images of the object.
 20. Themethod of claim 14, further comprising receiving a first laser pulse;converting, with at least one beam splitter, the first laser pulse intoa first pulse train that comprises a plurality of sub-pulses evenlyseparated in time; temporally stretching and chirping each of thesub-pulses of the first pulse train; and illuminating the object withthe temporally-stretched and chirped sub-pulses to create the firstseries of the images of the object.
 21. The method of claim 14, furthercomprising splitting each image in the first series of images of theobject into first and second fractions, wherein superimposing thepseudo-random binary spatial pattern onto each image of the first seriesto produce the second series of spatially-encoded images comprisessuperimposing the pseudo-random binary spatial pattern onto the firstfraction of the first series of images of the object; and integratingand recording the second fraction of the first series of images of theobject as an additional raw image, wherein reconstructing the fifthseries of final images by processing the single raw CUSP image accordingto the image reconstruction algorithm comprises processing the singleraw CUSP image and the additional raw image according to the imagereconstruction algorithm.
 22. The CUSP system of claim 1, wherein thespatial encoding module comprises a digital micromirror device.
 23. TheCUSP system of claim 22, wherein the digital micromirror devicecomprises an array of micromirrors.